Q. 114.1( 52 Votes )

<span lang="EN-US

Answer :

Given A and B are symmetric matrix of same order

A = A’ eqn1


B = B’ eqn2


So, AB – BA = A’B’ – B’A’ (from 1 & 2)


AB –BA = (BA)’ – (AB)’ ()


AB – BA = (-1) ((AB)’ – (BA)’) (taking -1 common)


AB – BA = -(AB – BA)’ ()


Here we see that the relation between (AB – BA) and its transpose i.e. (AB – BA)’ is (AB –BA) = -(AB – BA)’, this implies that (AB – BA is a skew symmetric matrix.


Hence proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

<span lang="EN-USMathematics - Exemplar

<span lang="EN-USMathematics - Exemplar

Given <img Mathematics - Exemplar

<span lang="EN-USMathematics - Exemplar

<span lang="EN-USMathematics - Exemplar

<span lang="EN-USMathematics - Exemplar

For the followingMathematics - Board Papers

<span lang="EN-USMathematics - Exemplar

Use <span lang="EMathematics - Board Papers

Let <span lang="EMathematics - Exemplar